The effect of elastic and inelastic scattering on electronic transport in open systems

• Autorzy: Kulinowski Karol , Wołoszyn Maciej , Radecka Marta , Spisak Bartłomiej J.

Identyfikatory

DOI

10.2478/amcs-2019-0031

• Języki publikacji: EN

Abstrakty

EN

The purpose of this study is to apply the distribution function formalism to the problem of electronic transport in open systems, and to numerically solve the kinetic equation with a dissipation term. This term is modeled within the relaxation time approximation and contains two parts, corresponding to elastic or inelastic processes. The collision operator is approximated as a sum of the semi-classical energy dissipation term and the momentum relaxation term, which randomizes the momentum but does not change the energy. As a result, the distribution of charge carriers changes due to the dissipation processes, which has a profound impact on the electronic transport through the simulated region discussed in terms of the current–voltage characteristics and their modification caused by the scattering. Measurements of the current–voltage characteristics for titanium dioxide thin layers are also presented, and compared with the results of numerical calculations.

Słowa kluczowe

EN

kinetic equation; relaxation time approximation; scattering process

PL

równanie kinetyczne; czas relaksacji; proces rozpraszania

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2019
• Tom: Vol. 29, no. 3
• Strony: 427--437
• Opis fizyczny: Bibliogr. 47 poz., rys., wykr.

Twórcy

autor

Kulinowski Karol

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland

autor

Wołoszyn Maciej

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland

autor

Radecka Marta

• Faculty of Materials Science and Ceramics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland

autor

Spisak Bartłomiej J.

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland

Bibliografia

• [1] Bak, T., Nowotny, J. and Nowotny, M.K. (2006). Defect disorder of titanium dioxide, Journal of Physical Chemistry B 110(43): 21560–21567.
• [2] Ben Abdallah, N., Degond, P. and Genieys, S. (1996). An energy-transport model for semiconductors derived from the Boltzmann equation, Journal of Statistical Physics 84(1): 205–231.
• [3] Cabrera, R., Bondar, D.I., Jacobs, K. and Rabitz, H.A. (2015). Efficient method to generate time evolution of the Wigner function for open quantum systems, Physical Review A 92(4): 042122.
• [4] Caldeira, A.O. and Leggett, A.J. (1981). Influence of dissipation on quantum tunneling in macroscopic systems, Physical Review Letters 46(4): 211–214.
• [5] Chatterjee, K., Roadcap, J.R. and Singh, S. (2014). A new Green’s function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry, Journal of Computational Physics 276: 479–485.
• [6] Chruściński, D. and Pascazio, S. (2017). A brief history of the GKLS equation, Open Systems and Information Dynamics 24(3): 1740001.
• [7] Costolanski, A.S. and Kelley, C.T. (2010). Efficient solution of the Wigner–Poisson equations for modeling resonant tunneling diodes, IEEE Transactions on Nanotechnology 9(6): 708–715.
• [8] Danielewicz, P. (1984). Quantum theory of nonequilibrium processes I, Annals of Physics 152(2): 239–304.
• [9] Di Ventra, M. (2008). Electrical Transport in Nanoscale Systems, Cambridge University Press, Cambridge.
• [10] Ferry, D.K., Goodnick, S.M. and Bird, J. (2009). Transport in Nanostructures, Cambridge University Press, Cambridge.
• [11] Frensley, W.R. (1990). Boundary conditions for open quantum systems driven far from equilibrium, Reviews of Modern Physics 62(3): 745–791.
• [12] Fujita, S. (1966). Introduction to Non-Equilibrium Quantum Statistical Mechanics, W.B. Saunders Company, Philadelphia, PA.
• [13] Gómez, E.A., Thirumuruganandham, S.P. and Santana, A. (2014). Split-operator technique for propagating phase space functions: Exploring chaotic, dissipative and relativistic dynamics, Computer Physics Communications 185(1): 136–143.
• [14] Hong, S. and Jang, J. (2018). Transient simulation of semiconductor devices using a deterministic Boltzmann equation solver, IEEE Journal of the Electron Devices Society 6: 156–163.
• [15] Hong, S.-M., Pham, A.-T. and Jungemann, C. (2011). Deterministic Solvers for the Boltzmann Transport Equation, Springer Science & Business Media, Vienna.
• [16] Jacoboni, C., Bertoni, A., Bordone, P. and Brunetti, R. (2001). Wigner-function formulation for quantum transport in semiconductors: Theory and Monte Carlo approach, Mathematics and Computers in Simulation 55(1–3): 67–78.
• [17] Jacoboni, C., Poli, P. and Rota, L. (1988). A new Monte Carlo technique for the solution of the Boltzmann transport equation, Solid-State Electronics 31(3): 523–526.
• [18] Jonasson, O. and Knezevic, I. (2015). Dissipative transport in superlattices within the Wigner function formalism, Journal of Computational Electronics 14(4): 879–887.
• [19] Kim, K.-Y. (2007). A discrete formulation of the Wigner transport equation, Journal of Applied Physics 102(11): 113705.
• [20] Kim, K.-Y. and Kim, S. (2015). Effect of uncertainty principle on the Wigner function-based simulation of quantum transport, Solid-State Electronics 111: 22–26.
• [21] Kohn, W. and Luttinger, J.M. (1957). Quantum theory of electrical transport phenomena, Physical Review 108(3): 590–611.
• [22] Kulczycki, P., Kacprzyk, J., Kóczy, L., Mesiar, R. and Wisniewski, R. (2019). Information Technology, Systems Research, and Computational Physics, Springer, Cham, (in press).
• [23] Kulczycki, P., Kowalski, P. and Łukasik, S. (Eds) (2018). Contemporary Computational Science, AGH-UST Press, Cracow, p. 4.
• [24] Leaf, B. (1968). Weyl transformation and the classical limit of quantum mechanics, Journal of Mathematical Physics 9(1): 65–72.
• [25] Lee, H.-W. (1995). Theory and application of the quantum phase-space distribution functions, Physics Reports 259(3): 147–211.
• [26] Lifshits, I.M., Gredeskul, S.A. and Pastur, L.A. (1987). Introduction to the Theory of Disordered Systems, John Wiley and Sons, Inc., New York, NY.
• [27] Luttinger, J.M. and Kohn, W. (1958). Quantum theory of electrical transport phenomena II, Physical Review 109(6): 1892–1909.
• [28] Mahan, G.D. (2000). Many Particle Physics, Kluwer Academic Plenum Publishers, New York, NY.
• [29] Muscato, O. and Wagner, W. (2016). A class of stochastic algorithms for the Wigner equation, SIAM Journal on Scientific Computing 38(3): A1483–A1507.
• [30] Nedjalkov, M., Kosina, H., Selberherr, S., Ringhofer, C. and Ferry, D.K. (2004). Unified particle approach to Wigner–Boltzmann transport in small semiconductor devices, Physical Review B 70(11): 115319.
• [31] Nedjalkov, M., Selberherr, S., Ferry, D., Vasileska, D., Dollfus, P., Querlioz, D., Dimov, I. and Schwaha, P. (2013). Physical scales in theWigner–Boltzmann equation, Annals of Physics 328: 220–237.
• [32] Nedjalkov, M. and Vitanov, P. (1989). Iteration approach for solving the Boltzmann equation with the Monte Carlo method, Solid-State Electronics 32(10): 893–896.
• [33] Nowotny, J., Radecka, M. and Rekas, M. (1997). Semiconducting properties of undoped TiO2, Journal of Physics and Chemistry of Solids 58(6): 927–937.
• [34] Querlioz, D. and Dollfus, P. (2010). The Wigner Monte-Carlo Method for Nanoelectronic Devices: A Particle Description of Quantum Transport and Decoherence, ISTE Ltd. and John Wiley and Sons, Inc., New York, NY.
• [35] Rammer, J. (2007). Quantum Field Theory of Non-Equilibrium States, Cambridge University Press, Cambridge.
• [36] Schieve, W.C. and Horwitz, L.P. (2009). Quantum Statistical Mechanics, Cambridge University Press, Cambridge.
• [37] Schleich, W.P. (2001). Quantum Optics in Phase Space, John Wiley and Sons, Inc., New York, NY.
• [38] Schulz, D. and Mahmood, A. (2016). Approximation of a phase space operator for the numerical solution of the Wigner equation, IEEE Journal of Quantum Electronics 52(2): 1–9.
• [39] Sellier, J., Amoroso, S., Nedjalkov, M., Selberherr, S., Asenov, A. and Dimov, I. (2014). Electron dynamics in nanoscale transistors by means of Wigner and Boltzmann approaches, Physica A: Statistical Mechanics and Its Applications 398: 194–198.
• [40] Sellier, J. and Dimov, I. (2014). The Wigner–Boltzmann Monte Carlo method applied to electron transport in the presence of a single dopant, Computer Physics Communications 185(10): 2427–2435.
• [41] Spisak, B.J., Wołoszyn, M. and Szydłowski, D. (2015). Dynamical localisation of conduction electrons in one-dimensional disordered systems, Journal of Computational Electronics 14(4): 916–921.
• [42] Stashans, A., Lunell, S. and Grimes, R.W. (1996). Theoretical study of perfect and defective TiO2 crystals, Journal of Physics and Chemistry of Solids 57(9): 1293–1301.
• [43] Tatarskii, V.I. (1983). The Wigner representation of quantum mechanics, Soviet Physics Uspekhi 26(4): 311–327.
• [44] Ter Haar, D. (1961). Theory and applications of the density matrix, Reports on Progress in Physics 24(1): 304–362.
• [45] Thomann, A. and Borz, A. (2017). Stability and accuracy of a pseudospectral scheme for the Wigner function equation, Numerical Methods for Partial Differential Equations 33(1): 62–87.
• [46] Wigner, E. (1932). On the quantum correction for thermodynamic equilibrium, Physical Review 40(5): 749–759.
• [47] Zurek, W.H. (2003). Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics 75(3): 715–775.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).